On characteristics of K0 value and shear behaviour of loess using triaxial test

Compared with conventional soils, such as sand and clay, little knowledge on the coefficient of lateral earth pressure at-rest (K0) has been established for loess in the current literature. This paper presents an experimental investigation on K0 of compacted loess and the associated impacts on undrained shear behaviour. By adopting a K0 consolidation module in the triaxial system, the K0 stress state for loess samples was achieved through a unique feedback control. During the K0 consolidation, the deviatoric stress (q) increases progressively with the premise that the volumetric strain (εv) of the sample equals to the axial strain (εa). The results show that the K0 value of compacted loess is in a range of 0.28 to 0.53, which is dependent on the packing density and the clay content. A distinguishable decrease of K0 was found in the course of K0 consolidation for the loosely compacted loess sample, whereas a similar trend was not observed in the dense sample. In the undrained shear stage, all loess specimens revealed contractive response in the stress path (q-p’) diagram, which can be quantified by a modified collapsibility index (Ic). The index is consistently higher for the K0 consolidated loess samples than for the isotropic ones. The experimental results indicate a strong impact of the initial stress state on the shear behaviour of compacted loess.


Experimentation Test material and sample preparation
The loess used in the test was sampled in Yan'an City, Shaanxi Province, China, with an in-suit natural void ratio of 0.77 and a natural moisture content of 12%.Figure 2 shows the particle size distribution curve of the loess measured by sieving and sedimentation tests along with an image at the microscale, and it has a clay content of 10.5% by mass.As seen in Fig. 2b, two main forms of clay particles are visible in the image, namely clay-particle agglomerates and clay.In the former one, clays tend to assemble around the big particle with face contacts and point contacts, forming the interlocking pores.To evaluate the effect of clay content on K 0 , an extra amount of clay mainly composed of illite and montmorillonite was mixed with the loess, and the maximum clay content increases to 20%.Other physical properties of the test materials are also summarized in Table 1.
In this study, loess samples were prepared by the moist tamping (MT) method in conjunction with the undercompaction technique 20,21 .This method was selected because it is perhaps the best way to mimic the process of earth-fill project in the field, and it can produce high quality samples without segregation of particles 22 .As shown in Fig. 3, to obtain a target void ratio using the MT method, a pre-determined mass of wet soil was deposited into a split mold and then it was subjected to continuous tamping until the target height of the layer was achieved, and the degree of under-compaction was varied linearly from the bottom to the top layer, with an under-compaction ratio of 1%.In Fig. 4, the compaction curve of the tested loess is presented.Given that the optimal water content    of the loess is around 12%, hence, an initial water content of 11.6% is at the dry side within 5% of the optimal water content, which is often required for the soil compaction in engineering practices.

Test procedures
After the sample preparation, each loess sample was placed into a triaxial chamber and subjected to a saturation process.In this study, cylindrical samples of 50 mm in diameter and 100 mm in height were used in a triaxial apparatus.All samples were saturated in two stages: initially by flushing the sample with carbon dioxide 21,23,25 and de-aired water, and then by applying a stepwise back pressure.To achieve the full saturation state, a Skempton B value (the ratio between an increment of confining pressure and the corresponding change in pore pressure) greater than 0.95 is required 24 .
In this study, tests were conducted with an automatic triaxial testing system (Fig. 5).By adopting a K 0 consolidation module in the triaxial system through a feedback control, the increment of deviatoric stress (q) was controlled with the premise that the volumetric strain (ε v ) of the sample equals to the axial strain (ε a ).Therefore, the samples can reach the K 0 stress state progressively.Here, ε a and ε v were determined from the readings of vertical linear variable differential transformer (LVDT) and change of back volume, respectively.To bring the specimens to a target effective horizontal stress (σ' 3 ), a slow loading rate of 3 kPa/hr was employed, thus the excess pore water pressure, if any, was very small and could be neglected.A local LVDT of high-precision (linear range of ± 2.5 mm with an accuracy of 1.6 μm) was mounted at mid-height position of the samples to check the K 0 stress state as to whether no lateral strain (ε r ) was developed.After reaching K 0 stress state, however, the increments of radial deformation remained zero.The K 0 consolidation stage was then followed by an undrained shear test.In order to ensure a clear response of pore water pressure in the shear stage, the strain rate was chosen to be 0.167 mm/ min.For comparison, a series of tests were also carried out on isotropically consolidated loess samples (Table 2).

Validation of K 0 stress state
It is noted that at the K 0 stress state for soils, no lateral strain was developed 26 .In this study, to reach the K 0 stress state, using membranes as the lateral confinement in the triaxial test is more challenging than using the  conventional oedometer test with the rigid wall.Therefore, prior to address the shear behaviour of loess, a pressing concern is to examine whether the premise of no lateral strain is fulfilled in the K 0 consolidation stage.
Figure 6a presents development of the ratio between the volumetric and axial strain with time.It is clear to see that a little fluctuation within a range of 0.95 and 1.05 occurs at the initial consolidation stage (4 h), and it is then followed by a steady trend with the ratio approaching to one.This finding implies that the lateral strain of the samples is not developed at the most of time in consolidation.Moreover, Fig. 6b plots the readings of the radial and volumetric strains with time for the specimens subjected to a target effective horizontal stress (σ' 3 = 100 kPa and 350 kPa) in the consolidation stage.It is seen that the tendency in the development of the radial strain has flattened out with consolidation time.Compared with the maximum volumetric strain of approximately 8%, the development of maximum radial strain is relatively small (less than 0.8%).The above observations strongly indicate a satisfactory performance of the feedback control using the K 0 module in the triaxial test system, such that a general validity to the K 0 consolidation state for loess has been achieved.K 0 consolidation path and K 0 values Figure 7 presents a set of test results in K 0 consolidation for loosely compacted loess samples (e 0 ≈ 0.775).It is seen that the change of effective horizontal stress (σ' 3 ) is smaller than effective vertical stress (σ' 1 , σ' 1 = q + σ' 3 ) and the slope in the diagrams indicates the change of K 0 .Interestingly, a temporary plateau with a stepwise increment of σ' 3 is consistently observed.An inflection point is marked in the diagram using a downward arrow.It    appears that the inflection point is not dependent on the target effective horizontal stress.At a higher effective stress level after the plateau, if any, σ' 3 continues to increase with σ' 1 .It should be noted that the K 0 value at the end of consolidation is usually taken as the representative value, while others are nominal K 0 values due to the effect of initial isotropic stress state 27 .K 0 consolidation of loess samples prepared at two different packing densities are compared in Fig. 8.A marked difference in Fig. 8a is that the dense sample does not exhibit a stepwise increment of σ' 3 .Accordingly, the changes of K 0 are revealed in Fig. 8b, showing that the K 0 value starts to decrease from a reference isotropic stress state with the elapsed time.The K 0 of the dense sample reduces as long as the load is applied and reaches a more or less constant value around 0.28, whereas the K 0 of the loose sample mildly reduces until an abrupt reduction taking place around 20 h after applying the loads.Evidently, the K 0 value is greater for the loose samples.Figure 8c shows the change of sample volume during the K 0 consolidation.An unexpected volume change in sample K-1 is observed, that is also accompanied with the abrupt change in K 0 value (Fig. 8b).
When we recalled from the fundamentals of soil mechanics, the observations in Fig. 8c are similar with the path for normal and over-consolidated soils.In brief, the initial path in K-1 is elastic and its slope is dictated by Poisson's ratio, while the latter part follows the plastic flow 28 .For a denser sample (K-2), the yield stress is greater.Hence, it is postulated that an increase of volume would occur, if a higher σ' 3 is applied to the dense sample.In addition, an alternative explanation at the micro scale is perhaps due to an internal collapse of pores in the loose samples, and it contributes to the marked volume change 29 .
Figure 9 presents the experimental results from the original loess and the loess-clay mixtures.Noting that the test materials in this diagram were prepared at the same initial void ratio (e 0 ≈ 0.60) and the target effective horizontal stress (100 kPa), so that the differences in K 0 value were solely attributed to the presence of additive clay.In general, the K 0 value in this diagram decreases with an increment of σ' 3 .The reduction of K 0 value is more severe in the original loess sample with lower clay content (K-2).In Table 2, the K 0 values of test materials are summarized and it varies between 0.28 to 0.49 with different clay contents.Given a general trend of clay

Undrained response analysis
In Fig. 10a, results of stress path are presented in q-p' diagram, and it demonstrates a contractive behaviour.Here, p' is the mean effective stress (p' = (σ' 1 + 2σ' 3 )/3).Noteworthy is that "K-1" and "K-2" are at the same effective horizontal stress level (σ' 3 ), yet the magnitudes of deviatoric stress at the start of shear stage are different.Known from the preceding analysis, it is attributed to the discrepancy of K 0 (Table 2).The dense sample (K-2) yields a greater q.A straight line is used to connect the stress origin and the final stress state (ultimate axial strain is greater than 25%) of original loess sample, and it is also known as the critical state line (CSL) in q-p' diagram 31,32 .It is seen that original loess specimens subjected to the K 0 consolidation have a unique the slope of the line is 1.62.Besides, the undrained responses of loess-clay mixtures are compared in Fig. 10b.Evidently, the sample with higher clay content exhibits lower deviatoric stress at the start of shear stage, and the strength at the critical state is also smaller.Besides, the undrained unstable state (UIS) line that characterizes the onset of flow deformation is given in Fig. 10b.Here, the UIS line in the stress space (q-p') is referred as the linear line passing through the peak point and the origin in each triaxial undrained shear test.In this plot, it can be seen that the slope angle of the UIS line, denoted as a stress ratio q/p' , increases with a reduction in the clay content.To examine the effect of K 0 stress state on the undrained behaviour while isolating other possible influencing factors, in Fig. 11, test results are compared at similar post-consolidation void ratios (e c ) and mean effective stress levels (p ' ) (R-1 vs. K-3; R-3 vs. K-1).At a given p ' , the peak q is higher for the loess sample subjected to the K 0 consolidation than that in isotropic consolidation.Besides, compared with the isotropic consolidated sample in Fig. 11, the K 0 consolidated sample yields a slightly dilative behaviour (dp' > 0) in the undrained condition at the beginning of the shear stage.
Here, the mean effective stress p' is determined as follow, where σ 1 ' is the major principal stress, σ 3 ' is the minor principal stress.
In the triaxial test, the following relationship can be obtained, where σ c the confining stress, q is the deviatoric stress, u is the pore pressure.By combing the Eq. ( 1), ( 2) and ( 3), When dq > 3du, it can be derived that dp' > 0. In Fig. 12, test results of dq and du from the sample K-1 and R-3 are compared.It is noted that the slope of the diagonal line represents the ratio of dq/du, and it equals to 3. Specifically, the diagonal line sets a benchmark.At the beginning of the shear test, the data from the K 0 consolidated sample are located above the line, indicating a slightly dilative behaviour with dp' > 0. Under otherwise similar conditions, the data for the isotropic-consolidated sample are located below this line, indicating a contractive behaviour.The findings in Fig. 12 provide a rational explanation on discrepancies of the effective stress path between the isotropic consolidated sample and the K 0 consolidated sample in Fig. 11.
(1) To quantify the degree of strain softening with reference to the initial static shear stress, a parameter I c , termed the modified collapsibility index, is introduced, following the concept of Sivathayalan and Vaid 33 as follows.
where q cs and q 0 are the deviator stress at the critical state and prior to the undrained shearing, respectively.When I c = 0, it corresponds to no strain softening and the soils would exhibit completely dilative behaviour.When I c is greater than one, it implies the critical state strength is lower than the initial static shear stress, and thus the triggering of a flow slide if equilibrium is disturbed by a small undrained perturbation.As indicated in Fig. 11, at a similar state in terms of the void ratio and the mean effective stress level, I c is consistently higher in the K 0 consolidated samples than in the isotropic consolidated ones.This observation implies that the K 0 consolidated loess samples are more susceptible to severe failures.

Conclusions
This paper aims to not only characterize the K 0 of compacted loess, but also to explore the undrained response with the presence of initial shear stress by using the triaxial test.Several major findings from the experimental results are summarized as follows: (1) the K 0 of loess samples is density-dependent.A distinguishable decrease of K 0 value is revealed in the course of K 0 consolidation for the relatively loose sample; (2) the increase of clay content in loess induces higher K 0 value; (3) I c is consistently higher in the K 0 consolidated samples, which implies that the K 0 consolidated samples are more susceptible to severe failures.This study suggests a pressing need to consider the K 0 value of compacted loess in a rigorous manner in geotechnical designs, and the associated impacts on the undrained response of loess should be taken into accounted properly.

Figure 1 .
Figure 1.Comparison of the commonly used methods for K 0 calculation.

Figure 2 .
Figure 2. The particle size distribution curve and microscopic image of the test material: (a) particle size distribution curves of test materials; (b) microscopic image of compacted loess.

Figure 3 .
Figure 3. Schematic illustration of moist tamping method in sample preparation (Step 1: mixing soil at target water content; Step 2: transferring soil into a split mould by layers; Step 3: rough the surface of layers and compaction; Step 4: disassemble mould).

Figure 6 .
Figure 6.Measurements of strain in loess samples during K 0 consolidation: (a) comparison of volumetric strain and axial strain; (b) comparison of radial strain and volumetric strain.

Figure 8 .
Figure 8.Comparison of K 0 consolidation for loess samples with different initial void ratios.

Figure 9 .Figure 10 .
Figure 9.Comparison of K 0 for loess samples with different clay contents.

Table 1 .
Basic physical properties of test materials.

Table 2 .
Summary of K 0 and isotropic consolidation on loess.